He started his playing career in his hometown, where he scored 40 goals between 1984 and 1988 and became the best goalscorer of the former Yugoslav league. After that, he moved to Dinamo Zagreb.

Šuker wore Dinamo's blue jersey 60 times and scored 34 goals, and in 1991 signed for Spanish side Sevilla. There he spent five seasons and played even with Diego Maradona. In over 150 matches at Sevilla, he scored 76 goals.

Quality performances in Andalusia resulted in the move to Santiago Bernabeu, to one of the greatest clubs in the world, Real Madrid. He was among the Kings until 1999, implementing 40 goals in Real's successes, and once being the club top scorer. During that time, Šuker won one league title, one domestic Supercup, one Champions League title and one Intercontinental Cup.

After leaving Madrid, he wore the jersey of one other European giant, Arsenal of London. His club appearances came to a close in West Ham United and in the end, 1860 München. Šuker retired in 2003.

Davor Šuker was also one of the key players on the international level. In the youth ranks of the former Yugoslavian team he rose to prominence with 15 goals, including the appearances at the U-20 World Cup in Chile 1987, where his team won the gold medal. Šuker was the second best goalscorer of the tournament. Three years later, he won silver at the European U-21 Championships in Russia, winning the award for the best player as well. In the Yugoslav senior team he was capped twice, scoring once.

Deepest impact, of course, Šuker had in the Croatian chequered jersey. With 45 goals in 69 matches, he is still the best goalscorer of the national team in history. At the World Cup in France 1998, Croatia finished third, and Šuker won the Golden Boot with six goals to his name, ahead of Batistuta and Vieri, who both scored five.

In the same year, Šuker came third in the FIFA Player of the Year list, and second in the France Football Golden Shoe awards.

Šuker's achievements were recognized in Croatia as well as abroad. On six occassions he was named the Croatian footballer of the year, and in the successful 1998, he was also named the Sportsman of the year. Šuker is also the owner of the Franjo Bučar National Sports Award.

Celebrating its 50th anniversary in 2003, European Football Federation (UEFA) included Davor Šuker in the list of Golden Players as the Croatian representative, based on the nomination by Croatian Football Federation. He also made the Pele's list of 125 best players of all time, as well as the distinguished World Soccer Magazine list of 100 best players of the 20th century.

After retiring, Šuker managed his own football academy, and in 2010 he became a member of the Croatian Football Federation Assembly. In 2011, he was appointed to the UEFA Football Committee.

On July 5th 2012, he was elected as the president of the Croatian Football Federation, an office he holds to this date. From August of the same year, he was also a member of the Organising Committee for the FIFA Confederations Cup.

On April 14th 2014, Šuker was re-elected as the president of the HNS with unanimous decision by the Assembly until 2018.

On March 24th 2015, Šuker was elected as the member of the UEFA Executive Committee, becoming the first Croatian in this governing body of UEFA. He was also put in charge as a chairman of the Football Committee and named as the deputy chairman of the Marketing Advisory Committee. 

Since 2017, Šuker is a member of the Organising committee for FIFA competitions. During his presidency, Croatia national team qualified for three major tournaments - FIFA World Cup 2014 in Brazil, UEFA EURO 2016 in France and FIFA World Cup 2018 in Russia, where Croatia national team won 2nd place, thus achieving the greatest result in the history of Croatian football.

Šuker was re-elected as the HNS president on 22 December 2017 for a new four-year term. In February 2019, Šuker was re-elected to the UEFA Executive Committee, receiving 47 votes from European national associations.